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Rioplatense Mathematical Olympiad, Level 3
2002 Rioplatense Mathematical Olympiad, Level 3
1
1
Part of
2002 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
\frac{a^2b+b}{ab^2+9} is an integer
Source: Rioplatense Olympiad 2002 level 3 P1
9/6/2018
Determine all pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of positive integers for which
a
2
b
+
b
a
b
2
+
9
\frac{a^2b+b}{ab^2+9}
a
b
2
+
9
a
2
b
+
b
is an integer number.
Integer
number theory
positive integers